Bulega began racing at the age of eight in the Italian Minimoto Championship. He claimed both the Italian and European MiniGP 50 championships in 2011, then won the Italian PreGP 125 title in 2012 and the PreGP 250 title in 2013. Those results earned him a place in the CEV Moto3 Championship, where he finished sixth overall as a rookie in 2014 before winning the FIM CEV Moto3 Junior World Championship in 2015.
Bulega made his Grand Prix debut at the 2015 Valencian Grand Prix with Sky Racing Team VR46 aboard a KTM. In 2016, his first full season in Moto3, he showed considerable potential, scoring his first pole position at Jerez and claiming a podium finish there. A 12-place grid penalty at Valencia that year cost him the Rookie of the Year award, which went to Joan Mir instead. He finished the championship in seventh place with 129 points.
The following two seasons in Moto3 proved difficult. In 2017 he finished 12th in the standings with 81 points, hampered by qualifying difficulties and poor starts partly attributed to his height. His 2018 campaign was worse still, with four straight retirements at the start of the year and only 18 points scored in total.
Sky VR46 nonetheless gave Bulega an opportunity in Moto2 for 2019, partnering Luca Marini. He managed four top-ten finishes but finished only 17th in the standings with 48 points. Two subsequent seasons with Federal Oil Gresini Moto2 also underwhelmed — 32 points in 2020 and a career-worst 12 points in 2021 — and Gresini did not retain him for 2022.
In September 2021, Bulega was announced as a rider for the Aruba.it Racing team in the 2022 Supersport World Championship on a Ducati. He finished fourth in the standings in his debut season, demonstrating strong potential in the category. In 2023, Bulega dominated the series, taking 14 wins and 18 podiums. He was crowned 2023 World Supersport Champion with three races still remaining, clinching the title after Race 1 at the Portuguese Round on 30 September.
Bulega stepped up to the Superbike World Championship in 2024 as Alvaro Bautista's teammate in the factory Aruba.it Racing Ducati squad. Despite it being his debut season in WorldSBK, he finished second in the championship, winning six races and taking 15 second-place finishes in a close battle with Toprak Razgatlioglu. In 2025, Bulega again finished as runner-up in the championship, this time accumulating 20 Superbike victories across the season.
Bulega also made a brief return to Grand Prix racing, replacing Marc Marquez for the final two races of the 2025 MotoGP season after testing the Ducati Desmosedici GP at Jerez. For 2026, Ducati hired him as a factory test rider alongside Michele Pirro, focused on development work related to the 2027 regulations, particularly on Pirelli tire performance.
Bulega's career trajectory — from a struggling Grand Prix rider to a dominant world-level champion and top WorldSBK contender — illustrates the impact of finding the right category and machinery. His back-to-back runner-up finishes at the WorldSBK elite level alongside Ducati's factory program confirm his standing as one of the leading figures in current international superbike racing.